Li Yelena Alex

On Rado Numbers for x + by = bz: The b^k Pattern and a Threshold Conjecture

For integers b >= 2 and k >= 1, let R_k(b) denote the k-color Rado number for the equation x + by = bz, defined as the least positive integer n such that every k-coloring of {1, 2, ..., n} contains a monochromatic solution. Under the substitution d = z - y, this equation is equivalent to x = bd, placing it in the famil...